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Advanced Numerical Methods in the Mathematical Sciences

Jie Du, University of Science and Technology of China
A Simple Weighted Essentially Non-Oscillatory (WENO) Limiter for the Correction Procedure via Reconstruction (CPR) Framework on Unstructured Meshes


We adapt a simple weighted essentially non-oscillatory (WENO) limiter, originally designed for discontinuous Galerkin (DG) schemes on two-dimensional unstructured triangular meshes, to the correction procedure via reconstruction (CPR) framework for solving nonlinear hyperbolic conservation laws on two-dimensional unstructured triangular meshes with straight or curved edges. This is an extension of our earlier work in which the WENO limiter was designed for the CPR framework on regular meshes. The objective of this simple WENO limiter is to simultaneously maintain uniform high order accuracy of the CPR framework in smooth regions and control spurious numerical oscillations near discontinuities. The WENO limiter we adopt in this paper uses information only from the target cell and its immediate neighbors. Hence, it is particularly simple to implement and will not harm the conservativeness and compactness of the CPR framework. Numerical results for both scalar equations and Euler systems of compressible gas dynamics are provided to illustrate the good behavior of this procedure.